Two weeks ago, after scoring an end of the first marking period test taken by two of my algebra 1 sections, thoughts of doom and despair entered my mind. Students obviously struggled with the content, as they averaged a 38% on the test. While they had seen nearly every problem either on an earlier quiz, homework assignment, in-class assignment, or lecture, and multiple “checks for understanding” indicated the majority (~80%) understood the concept or procedure, either they did not at the time, or their ability to recall and apply what they learned afterwards diminished significantly. Six weeks of effort meant to establish a level foundation for my students did not yield the results I expected. The enormity of the situation weighed heavily upon my mind. I could not continue on to the next series of topics: inequalities. Reteaching the content using the test as a guideline for my students seemed the only reasonable choice.
Clearing my mind of the devastation I felt, I carefully reviewed each section of the test with my students re-emphasizing the concept and procedures specific to each. Students had the initial test from which to review, and three full days reviewing the solutions both with me showing how, as well as various students who answered particular problems correctly. With this review completed, students took a nearly identical test, with certain problems the same on the retake as on the initial test.
Unfortunately, when scoring the retakes, a similar feeling crept into the fore. With nothing to substantiate the feeling other than the incorrect marks on each test, and the stack of scored tests showing total points lost overall and per page, my initial impression was that students did not improve on the retake.
After entering their results into Excel, analyzing them, and creating various charts, I found a reason to remain hopeful. Yet, while they did improve, with an average score of 43%, I had hoped for more; the average score just barely topped the cut score I use to delineate a “far below basic” from a “below basic” level of understanding, which translates to an F and a D, respectively, come letter grade time. Nonetheless, between the two sections, they improved the average by five percentage points, or twenty-two percent. In magnitude, the 22% improvement sounds decent, however, as we started from such a low initial score, we remained at a low score after the retake. Notwithstanding the fact that we still had a long way to go for the majority of the class to achieve a basic level of understanding, we did improve scores, which deserved a small celebration, at least in terms of reigniting my passion to improve my students’ understanding of algebra so that they pass the course, and remain on track to graduate high school.
I plan to rally my students by celebrating their success, and explaining the situation and plan forward. At the same time, the sober fact that the average for the two sections remains nearly thirty percentage points from where I would like to be will keep the celebration short lived. The plan right after is to return to square one for these concepts so that retake part deux achieves a more significant improvement. This requires setting the pacing guide aside for a while, and likely even a revision to the guide. Fortunately, I have the latitude to do so as I helped create the pacing guide, which is based on the Common Core State Standards. I originally planned to teach to the Common Core pacing guide once I established a more level playing field (of understanding and procedural fluency) for my students. The field is still quite uneven, so further review, reteaching, and relearning is required.
Skills and understanding intended to be established in elementary and middle school are holding these students back from attaining higher scores; surprisingly, over 90% of my algebra 1 students took algebra 1 in eighth grade, so these skills should have been re-established already. But they have not. Until the root cause for the various misunderstandings, misconceptions, or mistakes are identified and addressed, scores will remain stuck in the below basic and far below basic levels, which is insufficient for success with the richer content and process standards of the Common Core.
The following figures illustrate multiple aspects of the results. As one can see, initial and retake scores are nowhere near proficient for more than a few students.
Correlation Between Retake and Initial Scores
As the figure shows, a significant number of students improved on the retake, while others worsened slightly. The average gain shows clearly as the regression line nearly parallels the red line, which defines a line of perfect, positive correlation.
Initial and Retake Scores Per Student
Individual student scores ranged from exceedingly low to quite high. Many students improved upon their initial score. However, far too many, close to 80% of students, fall into the far below basic and below basic levels, which needs to be addressed before we move on with new content. I believe it may require two or more weeks to remedy, and this assumes full student engagement; in other words, students must want to master these concepts before scores improve significantly, irrespective of the length, or intensity of the review.
This figure underscores the enormity of the challenge facing us. Fortunately, there was positive movement in the three-day period, which I hope to build upon starting this coming Monday.
Wrapping up the various ways to view results of the retake, it is nice to see the decrease in far below basic scores and the accompanying increase in basic and advanced scores. Now, the challenge is to shift the entire distribution more to the right.
Test problems covered pre-algebra and beginning algebra topics spanning the following concepts.